Question

a scale shows a container’s weight to be 80.3 pounds. you need to know the weight of the container in kilograms. find this by completing the parts below. (a) let x be the unknown number of kilograms. using the values below, create a proportion that can be used to find x. use the conversion 1 kilogram = 2.2 pounds. values: x, 1, 2.2, 80.3 (b) use the proportion from part (a) to find the weight of the container in kilograms. do not round any computations.

Explanation:

Step1: Set up the proportion

We know that 1 kilogram is equal to 2.2 pounds. Let \( x \) be the weight in kilograms and 80.3 be the weight in pounds. The proportion should relate kilograms to pounds. So we set up the proportion as \(\frac{x}{80.3}=\frac{1}{2.2}\) (because the ratio of kilograms to pounds should be consistent).

Step2: Solve for \( x \)

To solve for \( x \), we can cross - multiply. Cross - multiplying gives us \( 2.2x = 80.3\times1\). Then, to find \( x \), we divide both sides of the equation by 2.2. So \( x=\frac{80.3}{2.2}\).

Answer:

For part (a), the proportion is \(\frac{x}{80.3}=\frac{1}{2.2}\). For part (b), \( x = \frac{80.3}{2.2}=36.5\) (if we were to calculate the value, but since we don't round, the exact form is \(\frac{80.3}{2.2}\) or we can write it as \(x=\frac{803}{22}\) after multiplying numerator and denominator by 10 to eliminate the decimal).